Properties

Label 2.7.ag_x
Base Field $\F_{7}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.308124534521$, $\pm0.308124534521$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25 3025 144400 6125625 281400625 13698361600 675593583025 33226866275625 1629189528768400 79810642935450625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 60 416 2548 16742 116430 820346 5763748 40372832 282540300

Decomposition

1.7.ad 2

Base change

This is a primitive isogeny class.